Question

2. A series of five constant dollar (or real-dollar) payments, beginning with $6,000 at the end of the first year, are increasing at the rate of 5% per year. Assume that the average general inflation rate is 4%, and the market interest rate is 11% during this inflationary period. What is the equivalent present worth of the series

Answer 1

Answer:

The equivalent present worth of the series is $27,211.16.

Explanation:

The first thing to do is to calculate the real interest using the following formula:

1 + i = (1 + r)(1 + inf) ..................... (1)

Where;

i = market interest rate = 11%, or 0.11

r = real interest rate = ?

inf = average general inflation rate = 4%, or 0.04

Substituting the values into equation (1) and solve for r, we have:

1 + 0.11 = (1 + r)(1 + 0.04)

1 + r = 1.11 / 1.04

1 + r = 1.06730769230769

r =  1.06730769230769 – 1

r = 0.06730769230769

The equivalent present worth of the series can now be calculated using the formula for calculating the present value (PV) of a growing annuity as follows:

PVga = (P / (r - g)) * (1 - ((1 + g) / (1 + r))^n) .................... (2)

Where;

PVga = present value of a growing annuity or equivalent present worth of the series = ?

P = constant dollar (or real-dollar) payments = $6,000

r = real interest rate = 0.06730769230769

g = growth rate of payments = 5%, or 0.05

n = number of years = 5

Substituting the values into equation (2), we have:

PVga = (6000 / (0.06730769230769 - 0.05)) * (1 - ((1 + 0.05) / (1 + 0.06730769230769))^5)

PVga = 346,666.666666712 * 0.078493722845371

PVga = $27,211.16

Therefore, the equivalent present worth of the series is $27,211.16.